Sequential water wave reconstruction in VOF-based numerical wave tanks with the EnKF approach

Existing phase-resolved wave reconstruction methods are mostly based on potential flow theory, which limits their ability to capture strongly nonlinear phenomena such as wave breaking dynamics. In such cases, the importance of multiphase incompressible Navier--Stokes solvers becomes particularly evident. These solvers form the foundation of the widely used numerical wave tanks in marine, ocean, and coastal engineering. However, the high dimensionality of the state variables in such systems often hinders the efficiency of data assimilation. The POD method is applied to reduce the order of the state vector in ensemble-based data assimilation, where instantaneous snapshots are naturally available. Given the unsteady nature and random phase combinations of irregular waves, the effectiveness of single data assimilation is limited. Sequential data assimilation is thus adopted to continuously update the wave profile as it evolves, ensuring that the wave field matches the real-world conditions. Therefore, inflation is needed to mitigate the ensemble collapse. Unlike single-phase flows without any interface, where the background error covariance can be inflated directly, to preserve physical constraints, when inflating for the phase field, the velocity field is simultaneously updated by incorporating potential flow formulas. Three representative cases-regular waves, irregular waves, and plunging waves-are used to validate the proposed method and assess its performance. The effect of assimilation parameters is also examined. The results demonstrate that the sequential data assimilation strategy achieves accurate free-surface reconstruction for a VOF-based numerical wave tank.